Method, module and system for analysis of physiological signal

ABSTRACT

The present disclosure provides a non-transitory computer program product embodied in a computer-readable medium, and when executed by one or more analysis module, providing a visual output for presenting physiological signals of a cardiovascular system. The non-transitory computer program product comprises a first axis representing subsets of intrinsic mode functions (IMFs); a second axis representing a function of signal strength in a time interval; and a plurality of visual elements, each of the visual elements being defined by the first axis and the second axis, and each of the visual elements comprising a plurality of analyzed data units collected over the time interval.

CROSS-REFERENCE TO RELATED APPLICATION

The present disclosure claims the benefit of U.S. provisional patentapplication No. 62/596,912, filed on Dec. 11, 2017, the entirety ofwhich is incorporated herein by reference.

FIELD

The present disclosure is generally related to the method, module andsystem for analysis of physiological signal. More particularly, thepresent disclosure is directed to a method, module and system foranalysis of electrical activities of the cardiovascular system.

BACKGROUND

Physiological signals provide valuable information for evaluation,diagnosis, or even prediction of physical conditions of a livingorganism. Each type of physiological signals obtained from a livingorganism represents the status of a particular system of the livingorganism.

Various physiological signals can be obtained from a living organism,including but not limited to: electrocardiography (EKG) signals,electromyography (EMG) signals, electroretinography (ERG) signals, bloodpressure, pulse oximetry (SpO₂) signals, body temperature, andspirometry signals. A plurality of metrics can be obtained frommeasurement of one or more physiological signals, including but notlimited to: electric current, electric impedance, pressure, flow rate,temperature, vibration, breath rate, weight, pulse amplitude, pulse wavevelocity, or frequency of physiological events. Also, the metrics can berecorded in a time varying fashion. Metrics can be measured by one ormore devices and then stored as the physiological signals. Thephysiological signals can be further processed into quantitative orqualitative information that are important in clinical evaluation,diagnosis, staging or prognosis.

Physiological signals may be presented by a graph with signal strengthor power over time, such as EKG or EMG. However, in frequencies or wavecharacteristics shown in the graph, noise or disturbances are consideredas irrelevant information when conducting analysis of acquired metrics.Moreover, wave patterns hidden in the acquired metrics could be areference for clinical evaluation, diagnosis, staging or prognosis.Thus, signal processing is a vital part for visualizing and extractinguseful information from physiological measurements.

The non-stationary and non-linear nature of many physiological wavesignals pose significant obstacles for signal processing. Conventionalapproaches for signal processing of physiological wave signals havefailed to provide an effective solution to the obstacles. For instance,Fourier transformation are often used to interpret linear and stationarywave signals, such as spectrum analysis; however, due to itsmathematical nature and probability distribution, Fourier transformationis unable to provide meaningful visualization results fromnon-stationary and non-linear wave signals.

Another conventional approach for signal analysis is the probabilitydistribution function. The probability distribution function is anothertool for study non-deterministic phenomena. Nevertheless, the signalsdescribed by conventional probability distribution function need to bestationary and with large amplitude variations. Conventional probabilitydistribution function is unable to provide insights from non-stationaryand non-linear wave signals.

The Holo-Hilbert spectral analysis (HOSA) is a tool for visualizingnon-stationary and non-linear waves. The mathematics behind HOSA hasbeen summarized in Huang et al (Huang, N. E., Hu, K., Yang, A. C.,Chang, H. C., Jia, D., Liang, W. K., Yeh, J. R. Kao, C. L., Juan, C. H.,Peng, C. K. and Meijer. J. H. (2016). On Holo-Hilbert spectral analysis:a full informational spectral representation for nonlinear andnon-stationary data. Phil. Trans. R. Soc. A, 374(2065)). HOSA adoptssome of the mathematical methodologies of Hilbert-Huang transformationwhen analyzing non-stationary and non-linear waves. However, theapplication of HOSA on analysis of EKG signals has never been exploredand exploited.

Due to the lack of adequate signal processing tools, data associatedwith acquired physiological signals often need to be analyzed by trainedprofessionals, in addition to available algorithms or software embeddedinstruments. Physiological measurement data could be massive in terms oftheir quantity and complexity. For instance, a Holter monitor cangenerate EKG data of an individual continuously for 24 hours. Thecomplexity and amount of the acquired 24-hour EKG data are overwhelmingeven for well-trained professionals, therefore increasing the chances ofmissed detection or misinterpretation of EKG deviation or abnormal EKGsignals.

Given the non-linear and non-stationary nature, and the inherentcomplexity and quantity of physiological signals of the cardiovascularsystem, there is a need for an efficient and intuitive mean for analysisand visualization of EKG. Specifically, a novel probability distributionfunction and a multiscale entropy generated by HOSA are proposed in thepresent disclosure to reveal the subtlety and nuance of the variationsin physiological signals.

SUMMARY OF THE INVENTION

It is an object of the present disclosure to provide HOSA-based methodsand systems for analysis of physiological signals of the cardiovascularsystem.

It is an object of the present disclosure to provide one or more visualoutputs of electrocardiography (EKG) signals, electromyography (EMG)signals, or blood pressure signals.

It is also an object of the present disclosure to provide one or morevisual outputs of abnormal EKG, EMG, or blood pressure.

It is also an object of the present disclosure to provide one or morevisual outputs to compare physiological signals of the cardiovascularsystem in different groups of subjects, different subjects, or differenttime intervals of the same subjects.

It is also an object of the present disclosure to provide applicationsof HOSA in diagnosis of cardiovascular system diseases.

An embodiment of the present disclosure provides a non-transitorycomputer program product embodied in a computer-readable medium, andwhen executed by one or more analysis module, providing a visual outputfor presenting physiological signals of a cardiovascular system. Thenon-transitory computer program product comprises a first axisrepresenting subsets of intrinsic mode functions (IMFs); a second axisrepresenting a function of signal strength in a time interval; and aplurality of visual elements, each of the visual elements being definedby the first axis and the second axis, and each of the visual elementscomprising a plurality of analyzed data units collected over the timeinterval. Wherein each of the analyzed data units comprises a firstcoordinate, a second coordinate, and a probability density valuegenerated from an intrinsic probability density function of one of thesubsets of IMFs, the first coordinate is one of the subsets of IMFs, andthe second coordinate is an argument of the function of signal strength.

In a preferred embodiment, the second axis is a standard deviation or az-value of the signal strength in the time interval.

In a preferred embodiment, the probability density value is generatedfrom a subset of primary IMFs of secondary IMFs, each of the primaryIMFs is generated from an empirical mode decomposition (EMD) of aplurality of the physiological signals, and each of the secondary IMFsis generated from an EMD of the primary IMF.

In a preferred embodiment, the physiological signals are EKG signals,EMG signals, or blood pressure signals.

In a preferred embodiment, the probability density value is indicated bydifferent colors, grayscales, dot densities, contour lines, orscreentones.

Another embodiment of the present disclosure provides a system foranalyzing the physiological signals of the cardiovascular system. Thesystem comprises a detection module for detecting the physiologicalsignals of the cardiovascular system; a transmission module forreceiving the physiological signals from the detection module andtransmitting the physiological signals to the analysis module; andanalysis module for generating a plurality of analyzed data sets fromthe physiological signals, each of the analyzed data sets comprising aplurality of analyzed data units; and a visual output module forrendering a visual output space according to the analyzed data setsgenerated by the analysis module, and displaying a visual output.Wherein the visual output comprises a first axis representing subsets ofintrinsic mode functions (IMFs), a second axis representing a functionof signals strength in a time interval, and a plurality of visualelements defined by the first axis and the second axis, and each of thevisual elements comprises a first coordinate, a second coordinate, and aprobability density value generated by an intrinsic probability densityfunction of one of the subsets of IMFs, the first coordinate is one ofthe subsets of IMFs, and the second coordinate is an argument of thefunction of signal strength.

Another embodiment of the present disclosure provides a non-transitorycomputer program product embodied in a computer-readable medium, andwhen executed by one or more analysis modules, providing a visual outputfor presenting physiological signals of a cardiovascular system. Thenon-transitory computer program product comprises a first axisrepresenting a scale of intrinsic multiscale entropy (iMSE); a secondaxis representing cumulative IMFs; and a plurality of visual elements,each of the visual elements being defined by the first axis and thesecond axis, and each of the visual elements comprising an analyzed dataunit collected over a time interval. Wherein each of the analyzed dataunits comprises a first coordinate of the first axis, a secondcoordinate of the second axis, and an iMSE value generated from theIMFs.

In a preferred embodiment, the IMFs are a set of primary IMFs or a setof secondary IMFs, each of the primary IMFs is generated from an EMD ofa plurality of the physiological signals, and each of the secondary IMFsis generated from an EMD of the primary IMF.

In a preferred embodiment, the iMSE value is indicated by differentcolors. grayscales, dot densities, contour lines, or screentones.

Another embodiment of the present disclosure provides a system foranalyzing the physiological signals of the cardiovascular system. Thesystem comprises a detection module for detecting the physiologicalsignals of the cardiovascular system; a transmission module forreceiving the physiological signals from the detection module andtransmitting the physiological signals to the analysis module; ananalysis module for generating a plurality of analyzed data sets fromthe physiological signals, each of the analyzed data sets comprising aplurality of analyzed data units; and a visual output module forrendering a visual output space according to the analyzed data setsgenerated by the analysis module, and displaying a visual output.Wherein the visual output comprises a first axis representing a scale ofiMSE. a second axis representing cumulative IMFs, and a plurality ofvisual elements defined by the first axis and the second axis, and eachof the visual elements comprising an analyzed data unit collected over atime interval and each of the analyzed data units comprises a firstcoordinate of the first axis, a second coordinate of the second axis,and an iMSE value generated from the IMFs.

BRIEF DESCRIPTION OF THE DRAWINGS

Implementations of the present technology will now be described, by wayof examples only, with reference to the attached figures.

FIG. 1 is a schematic diagram of a system for analyzing physiologicalsignals in accordance with an embodiment of the present disclosure.

FIG. 2 is a flow diagram of a method for analyzing physiological signalsin accordance with an embodiment of the present disclosure.

FIG. 3 is a flow diagram of a method for analyzing EKG signals inaccordance with an embodiment of the present disclosure.

FIG. 4 is a flow diagram of a method for analyzing blood pressure inaccordance with an embodiment of the present disclosure.

FIG. 5A is a flow diagram of transforming electrical activity signalsinto a set of primary intrinsic mode functions (IMFs); FIG. 5B is a flowdiagram of an interpolation process; FIG. 5C is a flow diagram ofempirical mode decomposition (EMD); FIG. 5D is a flow diagram ofsecondary IMFs generated from envelope functions; FIG. 5E is a flowdiagram of transforming primary IMFs into frequency modulation (FM)functions; and FIG. 5F is a flow diagram of transforming secondary IMFsinto amplitude modulation (AM) functions, in accordance with embodimentsof the present disclosure.

FIG. 6 is a schematic diagram of an analyzed data unit in accordancewith an embodiment of the present disclosure.

FIG. 7 is a conventional probability density function of white noise.Gaussian noise. the sum of the white noise and Gaussian noise, and theproduct of the white noise and Gaussian noise.

FIG. 8A-8F are visual outputs of intrinsic probability density functions(iPDF) of the white noise, Gaussian noise, the sum of the white noiseand Gaussian noise, and the product of the white noise and Gaussiannoise, in accordance with embodiments of the present disclosure.

FIG. 9A is a conventional time-intensity chart of additive andmultiplicative effects of the product and sum of the white noise; FIG.9B is a conventional Fourier spectra of additive and multiplicativeeffects of the product and sum of the white noise.

FIG. 10A-10B are visual outputs of iPDF of the product and sum of thewhite noise, in accordance with an embodiment of the present disclosure.

FIG. 11 is a schematic diagram of another analyzed data unit inaccordance with an embodiment of the present disclosure.

FIG. 12 is a graph of data points numbers and amplitude.

FIG. 13A-13D are iMSE representations of different groups with differentdisease states or different ages, in accordance with an embodiment ofthe present disclosure.

FIG. 14A-14F are iMSE representations of contrasts between differentgroups shown in FIG. 13A-13D, in accordance with an embodiment of thepresent disclosure.

DETAILED DESCRIPTION

It will be noted at the beginning that for simplicity and clarity ofillustration, where appropriate, reference numerals have been repeatedamong the different figures to indicate corresponding or analogouselements. In addition, numerous specific details are set forth in orderto provide a thorough understanding of the embodiments described herein.However, it will be understood by those of ordinary skill in the artthat the embodiments described herein can be practiced without thesespecific details. In other instances, methods, procedures and componentshave not been described in detail so as not to obscure the relatedrelevant feature being described. The drawings are not necessarily toscale and the proportions of certain parts may be exaggerated to betterillustrate details and features. The description is not to be consideredas limiting the scope of the embodiments described herein.

Several definitions that apply throughout this disclosure will now bepresented.

The term “coupled” is defined as connected, whether directly orindirectly through intervening components, and is not necessarilylimited to physical connections. The connection can be such that theobjects are permanently connected or releasably connected. The term“comprising,” when utilized, means “including, but not necessarilylimited to”; it specifically indicates open-ended inclusion ormembership in the so-described combination, group, series and the like.

Referring to FIG. 1, a system for analyzing the physiological signals inaccordance with an embodiment of the present disclosure is provided. Thesystem 1 comprises a detection module 10, a transmission module 20, ananalysis module 30 and a visual output module 40. The system 1 isconfigured to detect physiological signals, to analyze physiologicalsignals and to display graphical information of the analyzed results.The physiological signal may include but not limited to: EKG signals,EMG signals, ERG signals, blood pressure, pulse oximetry signals, bodytemperature, and spirometry signals. It is contemplated that the system1 may further comprise other electrical components or modules for betterperformance or user experience. For example, the system 1 may comprisean amplifier module or filter module to enhance signal to noise ratio bygaining signal strength within certain bandwidth and minimizing noisefrom environmental interference or baseline wandering. For example, thesystem 1 may comprise an analog-to-digital converter (ADC) for signaldigitization. For example, the system 1 may further comprise a storagemodule for storing the digital signals or storing the analyzed data. Inone example, the detection module 10 may further comprise a dataacquisition module. The data acquisition module is capable of executingthe functions of the amplifier module, ADC and the storage module.Furthermore, the system 1 may comprise a user input module for use tocontrol the system 1, such as a keyboard, a mouse, a touch screen, or avoice control device.

The detection module 10 is configured to receive the physiologicalsignals and to convert the physiological signals into electrical signal.The detection module 10 may convert cardiovascular activities, skeletalmuscle activities, or blood pressure into electrical signals. Thedetection module 10 may comprise one or more sensing components, and thesensing component can be a transducer or a blood pressure meter. Thetransducer may be a biopotential electrode to detect the electricalpotentials or a magnetoelectric transducer to detect the magneticfields. The blood pressure meter may be an oscillometric monitoringequipment. It is contemplated that a ground electrode may be paired withthe biopotential electrodes for measuring electrical potentialdifferences and additionally a reference electrode may be presented fornoise reduction. The detection module 10 may be applied on the surfaceof one or more specified regions of the living organism for thedetection of specific physiological signals. The specified regions mayinclude but not limited to: the chest for EKG, the skin above theskeletal muscle for EMG, or the skin above the vein for blood pressure.In one example, the detection module 10 comprises at least 10biopotential electrodes being positioned on the limbs and the chest ofthe human body. The biopotential electrodes could be wet (with salinewater or conducting gels) or dry electrodes.

The transmission module 20 is configured to receive the electricalsignals from the detection module 10 and deliver the signals to theanalysis module 30. The transmission module 20 may be wired or wireless.The wired transmission module 20 may include an electrical conductivematerial delivering the detected signal directly to the analysis module30 or to the storage module for processing by the analysis module 30thereafter. The detected signal may be stored in a mobile device, awearable device or transmitted wirelessly to a data processing stationthrough RF transmitters, Bluetooth, Wi-Fi or the internet. The mobiledevice can be a smartphone, a tablet computer. or a laptop. The wearabledevice can be a processor-embedded wristband, a processor-embeddedheadband, a processor-embedded cloth, or a smartwatch. It iscontemplated that the modules of the system 1 may be electricallycoupled within a compact device or may be located discretely and coupledtogether by wired or wireless communication network.

The analysis module 30 is configured to process the signal by a seriesof steps. The analysis module 30 may be a single microprocessor, such asa general purpose central processing unit, an application specificinstruction set processor, a graphic processing unit. afield-programmable gate array, a complex programmable logic device or adigital signal processor. The analysis module 30 comprises anon-transitory computer program product embodied in a computer-readablemedium. The non-transitory computer program product can be a computerprogram, an algorithm, or codes that can be embodied in thecomputer-readable medium. The analysis module 30 may comprise multiplemicroprocessors or processing units to execute the non-transitorycomputer program product embodied in the computer-readable medium, inorder to perform different functional blocks of the entire analysisprocess.

The visual output module 40 is configured to display the graphicalresults of the information generated by the analysis module 30. Thevisual output module 40 may be a projector, a monitor, or a printer forprojecting the analysis results. In the examples, the analysis result isa visual output with graphic representations, and can be displayed bythe visual output module 40 on a color monitor, be printed out on apaper or an electronic file, or be displayed on a grayscale monitor.

Referring to FIG. 2, a method for analyzing the physiological signals inaccordance with an embodiment of the present disclosure is provided. Themethod for analyzing the physiological signals may include the steps asmentioned below. The method comprises: detecting the physiologicalsignals as a detected signal S21, performing empirical modedecomposition (EMD) on the detected signal to obtain a set of primaryintrinsic mode functions (IMFs) S22. creating envelope functions of thecorresponding of IMF 523 a, performing EMD on the envelope functions toobtain sets of secondary IMF 524, performing a transformation on theplurality of primary IMFs to obtain the frequency modulation (FM)functions S23 b, performing a transformation on the plurality ofsecondary IMFs to generate the AM function S25, generating data setaccording to the FM function and the AM function S26, generating avisual output space S27. The EMD in S22 can be complete ensembleempirical mode decomposition (CEEMD), ensemble empirical modedecomposition (EEMD), masking EMD, enhanced EMD, multivariate empiricalmode decomposition (MEMD), noise-assisted multivariate empirical modedecomposition (NA-MEMD). The transformation in S23 b and S25 can beHilbert transform, Direct quadrature, inverse trigonometric function, orgeneralized zero-crossing.

Detecting the physiological signals as one or more detected signals S21is performed at the detection module. Referring to FIG. 3, thephysiological signal may be EKG signals, in accordance with anembodiment of the present disclosure. Referring to FIG. 4, thephysiological signal may be blood pressure, in accordance with anembodiment of the present disclosure. In one example, the detectedsignal may be acquired and stored by the data acquisition module in theform of electrical potential (preferably measured by voltage) withcorresponding temporal sequences. The detected signal may be stored as adetected data set comprising a plurality of detected data units and eachdetected data unit comprises at least a signal strength and a timeinterval. A sampling rate of the data acquisition module may determine atime interval of adjacent data. As illustrated in FIG. 1, the analysismodule 30 generates the analyzed data set from the detected signal andthe analyzed data set may be stored in the storage module for visualoutput module 40 thereafter. The analyzed data set comprises a pluralityof analyzed data units.

The processes S22, S23 a, S23 b, S25, S32. S33 a, S33 b, S35, S42, S43a, S43 b, and S45 are further elaborated in FIG. 5A to FIG. 5F, inaccordance with embodiments of the present disclosure. The detectedsignals are consequently transformed or decomposed into primary IMFs,secondary IMFs. envelope functions, AM functions, and FM functions.

Referring to FIG. 5A, a plurality of EMDs for detected signals areprovided in accordance with an embodiment of the present disclosure. Thedetected signal is transformed into a set of primary IMFs by EMDs. Theplurality of EMDs in FIG. 5A correspond to S22 of FIG. 2, S32 of FIG. 3,or S42 of FIG. 4. The EMD is a process comprising a series of siftingprocess to decompose a signal into a set of IMFs. For example, aplurality of primary intrinsic functions is generated from the detectedsignal by EMD. A sifting process generates an intrinsic function fromthe detected signals. For example, a first sifting process generates afirst primary IMF 51 b from the detected signal 51 a; a second siftingprocess generates a second primary IMF 51 c from the first primary IMF51 b; a third sifting process generates a third primary IMF 51 d fromthe second primary IMF 51 c; a mth sifting process generates a mthprimary IMF 51 n from the (m−1)th primary IMF 51 m. The number ofsifting processes is determined by stopping criteria. The stoppingcriteria may depend on the signal attenuation or the variation of themth primary IMF 51 n.

Furthermore, EMD may comprise masking procedure or noise (even pairs ofpositive and negative values of the same noise) addition procedure withvariable magnitude adapted for each sifting step to solve mode mixingproblems. It is contemplated that EMD may be achieved by ensembletechniques.

Referring to FIG. 5B, a plurality of interpolation processes is providedin accordance with an embodiment of the present disclosure. Theinterpolation processes in FIG. 5B correspond to S23 a in FIG. 2, S33 ain FIG. 3, or S43 a in FIG. 4. An envelope function is the interpolationfunction generated by an interpolation process from detected signals.The envelope function connects local extrema of the detected signals.Preferably, the envelope connects the local maxima of theabsolute-valued function of the detected signals. The interpolationprocess may be achieved via linear interpolation, polynomialinterpolation, trigonometric interpolation or spline interpolation,preferably cubic spline interpolation. The envelope functions in FIG. 5Bare generated from IMFs in FIG. 5A by the interpolation processes. Afirst envelope function 52 a may be generated from the first primary IMF51 a; a second envelope function 52 b may be generated from the secondprimary IMF 51 b; a third enveloped function 53 b may be generated fromthe third primary IMF 53 a; a (m−1)th envelope function 52 m may begenerated from the (m−1)th primary IMF 51 m; a mth envelope function 52n may be generated from the nth primary IMF 51 n.

Referring to FIG. 5C, a plurality of EMDs is provided in accordance withan embodiment of the present disclosure. The plurality of sets ofsecondary intrinsic functions are generated from the envelope functionsby EMD. The EMDs in FIG. 5C correspond to S24 in FIG. 2, S34 a in FIG.3, or S44 a in FIG. 4. The first set of secondary IMFs 53 a is generatedfrom the first envelope function 52 a; the second set of secondary IMFs53 b is generated from the second envelope function 52 b; the (m−1)thset of the plurality of secondary IMFs 53 m is generated from the(m−1)th envelope function 52 m; the mth set of the plurality ofsecondary IMFs 53 n is generated from the mth envelope function 52 n.

Referring to FIG. 5D, a plurality of sets of secondary IMFs are providedin accordance with an embodiment of the present disclosure. The mthenvelope function 52 n, the mth set of secondary IMFs 53 n, and thesecondary IMFs included in the mth set of secondary IMFs 53 n areillustrated in FIG. 5D. The mth envelope function 52 n in FIG. 5Bcomprises a first secondary IMF 54 a of the mth set of secondary IMFs 53n, a second secondary IMF 54 b of the mth set of secondary IMFs 53 n, athird secondary IMF 54 c of the mth set of secondary IMFs 53 n, a(n−1)th secondary IMF 54 m of the mth set of secondary IMFs 53 n, and anth secondary IMF 54 n of the mth set of secondary IMFs 53 n. Therefore,there are IMFs in a number of m (number of the plurality of sets ofsecondary IMF) multiplying n (number of individual secondary IMFs in aset of secondary IMF in FIG. 5D.

Referring to FIG. 5E and FIG. 5F, a series of transformation processesis provided in accordance with an embodiment of the present disclosure.The transformation process is to convert a function from real domain tocomplex domain. The transformation process comprises at least atransformation and a complex pair function formation. The transformationprocess may be a Hilbert transform, a direct-quadrature-zero transform,an inverse trigonometric function transform, or a generalizedzero-crossing transform. The complex pair function formation is tocombine the function as the real part of the complex pair function andthe transformed function as the imaginary part of the complex pairfunction.

In FIG. 5E, the FM functions are the complex pair functions generatedfrom the plurality of primary IMFs by a proper transformation process.The transformation processes in FIG. 5E correspond to S23 b in FIG. 2,S33 b in FIG. 3, or S43 b in FIG. 4. The first primary IMF 51 a istransformed into a first FM function 55 a by the transformation process;the second primary IMF 51 b is transformed into a second FM function 55b by the transformation process; the third primary IMF 51 c istransformed into a third FM function 55 c by the transformation process;and the mth primary IMF 51 n is transformed into a mth FM function 55 nby the transformation process.

In FIG. 5F, the AM functions are the complex pair functions generatedfrom the secondary IMFs by a series of transformation processes. Thetransformation processes in FIG. 5F correspond to S25 in FIG. 2, S35 inFIG. 3, or S45 in FIG. 4. The first secondary IMF 54 d of the first setof secondary IMFs may be transformed into a (1,1) AM function 56 d bythe transformation process; the second secondary IMF 54 e of the firstset of secondary IMFs is transformed into a (1,2) AM function 56 e bythe transformation process . . . and the nth secondary IMF 54 k of thefirst set of the secondary IMFs is transformed into a (1, n) AM function56 k by the transformation process. Furthermore, the nth secondary IMF54 n of the mth set of secondary IMFs may be transformed into a (m, n)thAM function 56 n by the transformation process.

Referring to FIG. 5G, components of an analyzed data unit is provided inaccordance with an embodiment of the present disclosure. In FIG. 5G, theanalyzed data unit 31 comprises a time interval 32, a first coordinate33, a second coordinate 34 and a signal strength value 35. In oneembodiment, the time interval 32 is a period of time when the detectionmodule detects the physiological signals, the first coordinate 33indicates instantaneous frequency of FM measured by frequency (Hertz),and the second coordinate 34 indicates instantaneous frequency of AMmeasured by frequency (Hertz). The signal strength value 35 may indicatesignal amplitude measured by electrical potential (voltage) orelectrical current (ampere) or may indicate signal energy measured byenergy strength per unit time interval (watt). For each analyzed dataunit within the time interval, the first coordinate 33 can be theargument of the mth FM functions 55 n in FIG. 5E at corresponding timeinterval; the second coordinate 34 can be the argument of the (m, n)thAM function 56 n in FIG. 5F at corresponding time interval; the signalstrength value 35 is the value of the envelope function at correspondingtime interval. Preferably, the second coordinate 34 is larger than thefirst coordinate 33.

Referring to FIG. 6, elements of an analyzed data unit is provided inaccordance with an embodiment of the present disclosure. In FIG. 6, theanalyzed data unit 60 comprises a probability density value 63, a firstcoordinate 61 and a second coordinate 62. The probability densityfunction (PDF) is a probability density function of one subset of theIMFs. The probability density value is the probability at a specificsignal strength value or at a specific instantaneous frequency. In oneexample, the first coordinate indicates the order number of one subsetof the IMFs and the second coordinate indicates the signal strengthvalue. In another example, the first coordinate indicates the z-valueand the second coordinate indicates the instantaneous frequency. Thesubset of IMFs may comprise one IMF component or the combination of atleast two different IMF components. The signal strength value mayindicate signal amplitude measured by electrical potential (voltage) orelectrical current (ampere) or may indicate signal energy measured byenergy strength per unit time interval (watt). In some examples, theinstantaneous frequency or the specific signal strength value may becentralized by mean and normalized by standard deviation.

The visual output space comprising a first axis, a second axis and aplurality of visual elements. Each visual elements may include one ormore analyzed data units within a certain range formed by the subsets ofIMFs and the probability density value. The visual output module rendersvisual output space according to the analyzed data set. It iscontemplated that a smoothing process may be applied to the visualoutput space for those visual elements with sparse data units.

A smoothing process may be applied to the visual output space for thevisual elements. The smoothing process may be Butterworth filter,exponential smoothing, Kalman filter, Kernal smoother, Laplaciansmoothing, moving average or other image smoothing techniques.

Following the methods, principles and transformation processesillustrated in FIG. 2-4, and FIG. 5A-5F, a plurality of embodiments fromphysiological signals are demonstrated in FIG. 8A-8D, FIG. 10A-10B, FIG.13A-13D, and FIG. 14A-14F.

As shown in FIG. 7, a conventional probability density function of whitenoise, Gaussian noise and the sum of the white noise and Gaussian noise,and the product of white noise and Gaussian noise is provided. The whitenoise and Gaussian noise are generated from simulation data. Thecalibration used in FIG. 7 is demonstrated by using a white noise of10,000 sample with a unity standard deviation value. A deterministicStokes type wave is exemplified with the model:y(t)=5*cos[2*π*t/100+0.5*sin(2*π*t/100)]. FIG. 7 illustratesconventional PDFs for the white noise, the additive sum and themultiplicative products with the deterministic wave. Large amplitude ofthe deterministic Stoke type wave has overwhelmed the white noise tomake the PDF of the sum bimodal, and the product super-Gaussian.

FIG. 8A-8F and FIG. 10A-10B are visual outputs of the iPDF, inaccordance with one or more embodiments of the present disclosure. Eachof the visual outputs in FIG. 8A-8F and FIG. 10A-10B comprise a firstaxis and a second axis. The first axis indicates the order numbers 1-11of one subset of the IMFs, and each order number indicates an IMFcomponent within a time interval. The second axis indicates signalstrength values normalized by standard deviation. Each of the IMFcomponent comprises a plurality of analyzed data units, and each of theanalyzed data units comprises a probability density value, a firstcoordinate indicating the IMF component, and a second coordinateindicating the standard deviation. Each of the probability densityvalues in FIG. 8A-8F and FIG. 10A-10B is generated from a subset ofprimary IMFs, and each of the primary IMFs are generated from an EMD, asillustrated in FIG. 5A. The probability density value can also begenerated from a subset of secondary IMFs, and the secondary IMFs aregenerated from the primary IMFs, as illustrated in FIGS. 5B and 5C. Thegrayscales of each of the analyzed data units represents the probabilitydensity value, with darker gray being probability density value of +0.1or probability density value of −0.1, white being probability densityvalue of 0, and intermediate grays between the above grayss beingintermediate probability density values.

Additionally, the probability density value in the visual outputs ofiPDF may be represented by different colors, dot density, or screentone.In one embodiment, the red color indicates probability density value of+0.1, the blue color indicates probability density value of −0.1, whitecolor indicates probability density value of 0, and intermediate colorsbetween the above colors indicate intermediate probability densityvalues. In one embodiment, the dot density may be higher for a largerprobability density value, and lower density for a smaller probabilitydensity value. In still another embodiment, the screentone with moregrids may represent larger probability density value, and the screentonewith more dots may represent smaller probability density value.Conversely, the colors, the grayscale, dot density, or screentone canhave different meanings for various levels of the probability densityvalue.

Referring to FIG. 8A, a visual output of the iPDF of the Gaussian whitenoise is presented with IMF components, in accordance with an embodimentof the present disclosure. Each column is an IMF component or one of thesubsets of IMFs, and each of the IMF component should have similarFourier spectrum, but some of their iPDF could deviate drastically fromthe Gaussian because of the limited size of the sample, which make thelast few IMFs lacks the sufficient degree of freedom. Of particularinterest is the first IMF from the white noise, which represents thehighest frequency waves near the Nyquist limit. Thus, each sample pointis either a maximum or a minimum that makes the PDF of the first IMFdecidedly bimodal.

Referring to FIG. 8B, a visual output of the iPDF of partial sum of thewhite noise is presented with IMF components, in accordance with anembodiment of the present disclosure. Each subset of IMF comprises thesum of a plurality of IMFs. In FIG. 8B, the distributions plotted as afunction of the time scale is uniformly Gaussian, except the first IMFis bimodal. The minor deviation shown here is the fluctuation due to thesize of the sampling. Larger sample would produce smoother results asdedicated by the probability law. In FIG. 8B, the results indeed confirmthe expectation for a white noise data, except the first IMF component.

Referring to FIG. 8C, a visual output of the iPDF of the sum of thewhite noise and the deterministic Stokes type wave is presented with IMFcomponents, in accordance with an embodiment of the present disclosure.The deterministic wave signal has a bimodal distribution. Othercomponents in FIG. 6C are still near Gaussian, except that EMD leakagehad caused some fluctuations.

Referring to FIG. 8D, a visual output of the iPDF of the partial sum ofthe white noise and the deterministic Stokes type wave is presented withIMF components, in accordance with an embodiment of the presentdisclosure. In FIG. 6D, the distribution for the first IMF is stillbimodal; the next three partial sums are nearly Gaussian as expected.The distribution changes abruptly at the fifth partial sum, when thedeterministic Stokes type wave comes into the sum. As its magnitude isoverwhelming, all the partial sums thereafter are all identicallybimodal.

Referring to FIG. 8E, a visual output of the iPDF of the product of thewhite noise and the deterministic Stokes type wave is presented with IMFcomponents, in accordance with an embodiment of the present disclosure.The iPDF is similar to the iPDF of white noise as shown in FIG. 8Aexcept that the PDF of the first IMF is no longer bimodal. Themodulation of a deterministic Stokes type wave has modified the range ofthe amplitude of the three point waves and render them nearly Gaussiandistributed. The modulation effect on all the other IMFs is to make thenext three IMFs slightly super-Gaussian.

Referring to FIG. 8F, a visual output of the iPDF of the product of thewhite noise and the deterministic Stokes type wave is presented with IMFcomponents, in accordance with an embodiment of the present disclosure.The iPDF are all highly super-Gaussian through all the time scales. Thedrastic difference between the additive and the multiplicative processesis clear: linear additive processes is simply superposition without anyinteractions between the wave and the white noise. The influence of thedeterministic wave may show up when the scale reach the wave periodlocally. The multiplicative process may influence all the IMF componentsglobally. Also, the multiplicative process may produce a globalsuper-Gaussian distribution.

Referring to FIG. 9A, the additive and multiplicative effects of twoGaussian distributed white noise signals are presented. It is difficultto distinguish between the additive and multiplicative processes by themorphology of the signals presented in time domain.

Referring to FIG. 9B, the Fourier spectra of the additive andmultiplicative effects of two Gaussian distributed white noise signalsare presented. Both spectra have a white spectral form. Therefore, fromthe Fourier spectral form, it is difficult to tell the differencebetween additive and multiplicative processes.

Referring to FIG. 10A, a visual output of the iPDF of the additiveeffects of two Gaussian distributed white noise signals are presented,in accordance with an embodiment of the present disclosure. Thedistribution is Gaussian except the first IMF.

Referring to FIG. 10B, a visual output of the iPDF of the multiplicativeeffects of two Gaussian distributed white noise signals are presented,in accordance with an embodiment of the present disclosure. Thedistribution is decisively super-Gaussian.

The calibration in FIG. 8A-8F and FIG. 9A-9B show that even forstationary processes, iPDF provides more information on the constitutingcomponents and the underlying mechanisms involved in the data generationprocesses: linear additive or nonlinearly multiplicative.

In the present disclosure, intrinsic multi-scale sample entropy (iMSE)may be applied for measurement of signal complexity. The complexity ofeach IMFs in different scales is useful for distinguishing among variousphysiological or disease states. The signal may be a physiologicalsignal, for example, blood pressure, electrocardiography (EKG) signals,or electromyography (EMG) signals.

Referring to FIG. 11, elements of another analyzed data unit areprovided in accordance with an embodiment of the present disclosure. InFIG. 11, the analyzed data unit 111 comprises a first coordinate 112, asecond coordinate 113, and an entropy value 114. The entropy value 114may be a sample entropy value or an approximate entropy value. Thesample entropy value is calculated according to one subset of the IMFsat a designated scale parameter. In one example, the first coordinate112 indicates the scale parameter. The second coordinate 113 indicatesthe order number of one subset of the IMFs. The subset of IMFs maycomprise one IMF component or the combination of at least two differentIMF components. In another example, the first coordinate 112 indicatesthe scale parameter, and the second coordinate 113 indicates cumulativeIMFs.

The visual output space comprising a first axis, a second axis and aplurality of visual elements. Each visual elements may include multipleanalyzed data units within a certain range formed by the subsets of IMFsand the probability density value. The visual output module rendersvisual output space according to the analyzed data set. A smoothingprocess may be applied to the visual output space for those visualelements with sparse data units. For example, the smoothing process maybe Butterworth filter, exponential smoothing, Kalman filter, Kernalsmoother, Laplacian smoothing, moving average or other image smoothingtechniques.

In FIG. 12, the sample entropy of a signal may be calculated as: log(patterns of length m)−log (patterns of length m+1). The scaleparameters may be adjusted for calculating sample entropy values atdifferent scale parameters.

MSE is based on approximate Entropy of a given data, X={x_(i), for i=1 .. . n}, defined as

$\begin{matrix}{{{E(X)} = {- {\sum\limits_{x_{i} \in \Theta}{{p\left( x_{i} \right)}\log \; {p\left( x_{i} \right)}}}}},} & (1)\end{matrix}$

where p(.) is the probability density function of a set of randomnumbers, Θ. The MSE is defined as the joint entropy for a set of indexedsequence of n random variables, {X_(i)}={X₁, . . . , X_(n)}, with a setof values θ₁, . . . , Θ_(n), respectively:

$\begin{matrix}{{E_{n} = {- {\sum\limits_{x_{i} \in \Theta_{l}}\mspace{14mu} {\ldots \mspace{14mu} {\sum\limits_{x_{n} \in \Theta_{n}}{{p\left( {x_{l},\ldots \mspace{14mu},x_{n}} \right)}\log \; {p\left( {x_{t},\ldots \mspace{14mu},x_{n}} \right)}}}}}}},} & (2)\end{matrix}$

where p(x₁, . . . , x_(n)) is the joint probability of the randomvariable, X₁, . . . . X_(n). As the MSE is defined in terms ofprobability density function, it requires the existence of a mean and avariance of the data. The probabilistic measure requirements limited theapplication of MSE to stationary data only.

In order to make MSE useful for the physiological signals, variousattempts were made to remove any possible trends from the data. But allof the attempts were ad hoc with no solid theoretical foundation orproper justifications. With the introduction of Multi-scale IntrinsicEntropy analysis from Yeh et al (Yeh, J. R., Peng, C. K., & Huang, N. E.(2016). Scale-dependent intrinsic entropies of complex time series.Phil. Trans. R. Soc. A, 374(2065), 20150204.) the EMD in Huang et al(Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q.,. . . & Liu, H. H. (1998, March). The empirical mode decomposition andthe Hilbert spectrum for nonlinear and non-stationary time seriesanalysis. In Proceedings of the Royal Society of London A: mathematical,physical and engineering sciences (Vol. 454, No. 1971, pp. 903-995). TheRoyal Society.) was introduced as the tool to remove the trend ofvarious scales systematically, for EMD endowed the resulting IMF's tohave this special property. The idea is explained as follows:

When any non-stationary and nonlinear is decomposed in Intrinsic ModeFunctions (IMF's) through EMD, we have

$\begin{matrix}{{{x(t)} = {\sum\limits_{j = t}^{n}{c_{j}(t)}}},} & (3)\end{matrix}$

where each c_(j)(t) is an IMF except the last one, which might be atrend if there is one. By definition, each IMF should be dyadicallynarrow band, symmetric with respect to zero-axis, and having the samenumbers of extrema as the of zero-crossings. Furthermore, byconstruction, the IMF component c_(j+1) is essentially derived from thetrend of c_(j). The Kolmogorov-Sinai (KS) type entropy for the specificintrinsic mode function is defined as

ΔE _(k) =E _(k+1) −E _(k)

where E_(k) is defined as the partial sum of IMF:

$\begin{matrix}{\sum\limits_{j = t}^{k}{{c_{j}(t)}.}} & (4)\end{matrix}$

Though the KS-type entropy is essentially the approximate the entropy ofthe single IMF component, the above definition is necessary to representthe influence of all other IMF's in the system, for the EMD expansion isnonlinear. Thus, this definition would include the some nonlinearsummation effects, albeit incompletely. The KS-type entropy, so defined,had successfully revealed the scale dependent variations and thecontribution of each IMF component to the total entropy; however, theresult shows no relationship with the properties of the total data as inthe original MSE as a measure of the whole system. The original MSEessentially emphasized the view of the trees rather than the wholeforest. Therefore, it is impossible to make comparisons in the spirit ofthe original MSE. Now, we will redefine a new Intrinsic MSE with thefollowing steps:

-   -   1. Generating a set of IMF by empirical mode decomposition        (EMD). The EMD may be any of its variations such as EEMD, CREMD,        AEMD, and other decomposition methods. One example is given in        Equation (3).    -   2. Providing the first set of random variables as the ascending        partial sums for k=1 . . . to n,

$\begin{matrix}{X_{k} = {\sum\limits_{j = 1}^{k}{{c_{j}(t)}.}}} & (5)\end{matrix}$

-   -   3. Calculating the Approximate Entropy, E_(k), for each X_(k),        for all k from 1 . . . to n.    -   4. Providing the second set of random variables as the        descending partial sums also for k=1 . . . to n.

$\begin{matrix}{Y_{n - k} = {\sum\limits_{j = k}^{n}{{c_{j}(t)}.}}} & (6)\end{matrix}$

-   -   5. Calculating the Approximate Entropy, F_(k), for each Y_(n-k),        for all k from 1 . . . to n.    -   6. Generating a two-dimensional plot comprising E_(k) and F_(k)        in a sequential order. This final result is the new Intrinsic        Multiscale Entropy (iMSE).    -   7. Generating a topographic iMSE. In case data from spatially        distributed multi-stations, a Topographic iMSE (TiMSE) can be        constructed to represent the spatial and temporal variation of        the underlying variation of the complexity condition.

In this new form, the iMSE and TiMSE would contain all the possiblepartial sums of the data in terms of EMD expansion, which wouldsystematically detrend any data, stationary or non-stationary, andproduce the full scale dependent MSE, temporally and spatially.

In some examples, it is important to point out that though, according totraditional physical science, the entropy is highest when the systemrepresents a white noise. In the spirit of MSE analysis, however, onlywhen systems with a mixture of both long and short scale correlationwould we have the most complex. This special property make the MSEuseful to quantify complexity in the living systems.

To illustrate the prowess of the new iMSE and TiMSE, simulated data andhuman physiologic data are used in the following examples.

In the present disclosure, iPDF and iMSE may be helpful for diagnosisamong various cardiovascular diseases and cardiovascular disorders. Thevisual outputs of the iPDF and iMSE can be used to compare 2 or morestates of different groups of people, different individuals, or the sameindividual. Specific visual output patterns of one or moreneurophysiological or neuropsychiatric disorders can be identified. Thespecific visual output patterns may comprise a disease state, a healthystate, a good prognosis state, or other patterns relevant to diagnosis,prognosis, clinical evaluation, or staging of the disease. Thecomparison between the specific visual output patterns may be used toidentify the difference between two groups of people with differentcardiovascular disorders, two groups of people with different diseasestage, two groups of people with different prognosis of disease, twoindividuals with different cardiovascular disorders, two individualswith different disease stage, two individuals with different prognosisof disease, or two different time intervals of the same individual. Thecomparison on specific patterns may lead to establish a model for theclinical evaluation, diagnosis, staging, or prognosis of thecardiovascular disorder.

A healthy state could be defined as a subject or a group of subjectswithout being diagnosed with particular disease(s) of interest. Adisease state could be defined as a subject or a group of subject beingdiagnosed with particular disease(s) of interest. The healthy state andthe disease state may be presented on the same subject on different timeintervals or be presented on different subjects.

The present disclosure will now be described more specifically withreference to the following exemplary embodiments, which are provided forthe purpose of demonstration rather than limitation.

In the following examples, iMSE may be applied to electrocardiography(ECG) to quantify the heart rate variability (HRV). It has been shownthat HRV contains rich information on inter-scale interactions of theneural and physiologic mechanisms of the cardiovascular system.Furthermore, the present disclosure have also demonstrated that iMSEcould separate the subtle difference between the groups of healthyelders from the young. The present disclosure uses the same data fromYeh et al (Yeh. J. R., Peng, C. K., & Huang, N. E. (2016).Scale-dependent intrinsic entropies of complex time series. Phil. Trans.R. Soc. A, 374(2065), 20150204.), on human heartbeat time series forsubjects with different physiological and pathologic conditions. Thesedata are available from various databases summarized by Goldberger et al(Goldberger, A. L., Amaral, L. A., Glass, L., Hausdorff, J. M., Ivanov,P. C., Mark, R. G., . . . & Stanley, H. E. (2000). PhysioBank,PhysioToolkit, and PhysioNet: components of a new research resource forcomplex physiologic signals. Circulation, 101(23), e215-e220.). A totalof 141 heartbeat time series with different physiological andpathological conditions, including healthy subjects (normal), agedsubjects and disease subjects, were studied. Specifically, 72 healthysubjects were acquired from normal sinus rhythm RR interval database andMIT-BIH normal sinus rhythm database; 44 subjects with congestive heartfailure (CHF) from congestive heart failure RR interval database andBIDMC congestive heart failure database; 25 recordings of patients withatrial fibrillation (AF) from MIT-BIH atrial fibrillation database. Thehealthy subjects were divided into two groups by age: 44 subjects withage over 60 (66.2±3.7) years old form the group of healthy elderly andthe other 28 subjects with age of 36.39±9.4 years old form the group ofhealthy young subjects. CHF patients were divided into two subgroupsbased on the severity of the disease according to the criteria of NewYork Heart Association functional classification: a CHF I-II group isthe less severe group, and another CHF III-IV group is the most severegroup.

Referring to FIG. 13A-FIG. 13D, iMSE representations of different groupswith different disease states or different ages are provided inaccordance with an embodiment of the present disclosure. The iMSErepresentations of the MSE means of all subjects in each group with theentropy increment matrixes are plotted in logarithmic coarse-grainingiMSE scale as x-axis and cumulative IMFs as y-axis. The cumulative IMFs1-1, 1-6, 1-12, 6-12, and 12 on the y-axis in FIG. 13A-13D usebi-directional methods to represent diverse characteristics of thecumulation processes: cumulation processes from high-frequency bands andor cumulation processes from low-frequency bands. Similar to theanalysis results of the simulated time series of fractional Gaussiannoise, intrinsic entropies contributed by each specific IMF wereevaluated with a specific coarse-graining scale. Furthermore, thespecific coarse-graining scale depends on the intrinsic time scale ofthe corresponding IMF, indicating that the specific coarse-grainingscale corresponding to the intrinsic entropy can be determined by theintrinsic time scale of the corresponding IMF. FIG. 13A is the iMSErepresentation of the heartbeat time series from the 28 healthy youngsubjects. FIG. 13B is the iMSE representation of the heartbeat timeseries from the 44 healthy old subjects. FIG. 13C is the iMSErepresentation of the heartbeat time series from the 44 subjects withCHF. FIG. 13D is the iMSE representation of the heartbeat time seriesfrom the 25 subjects with AF.

Importantly, without the troublesome detrend and filtering selectionshere, the iMSE representations in FIG. 13A-13D reveal clear differencesamong different groups: When comparing iMSE representations from thehealthy young subjects of FIG. 13A and the healthy elder subjects ofFIG. 13B, as the subjects age increase, the HRV complexity decreases inthe shorter scale but enhanced in the longer scale, reflecting aphysiologic reality of slowing down the reactions to environmentalchallenges. In the CHF group of FIG. 13C, their HRV complexitydeteriorate further.

In FIG. 14A-FIG. 14F, iMSE representations of contrasts betweendifferent groups are provided, in accordance with an embodiment of thepresent disclosure. Each of the iMSEs in FIG. 14A-14F is presented toidentify the contrast between two different groups from FIG. 13A, 13B,13C, or 13D. Regarding to the AF group, the original data is hard to bedistinguish from white noise, and the difference between the iMSErepresentations in FIG. 13B and FIG. 13D are difficult to identify,therefore it would be hard to separate the iMSE representation of the AFgroup and from the healthy elder subject group. To reveal the subtletybetween these groups, the iMSE is applied to examine the differencebetween the different groups given in FIG. 14A-FIG. 14F, in which allthe possible pairwise differences of the groups in FIG. 13A-13D arepresented. In FIG. 14A-14F, the differences are plotted in logarithmiccoarse-graining iMSE scale as x-axis and cumulative IMFs as y-axis,wherein the cumulative IMFs uses bi-directional methods to representdiverse characteristics of the cumulation processes, as shown in FIG.13A-13D. FIG. 14A presents the contrast between the healthy young andelder subject groups: the young show a greater entropy matrix in thefine-graining scale, and less entropy matrixes in the coarse-grainingscales as expected. FIG. 14B presents the contrast between the healthyyoung and the CHF group, the healthy young subject group has anoverwhelming greater complexity over all scales. FIG. 14C presents thecontrast between the healthy young subject group and the AF group.First, in a descending region of scale 20-30 and cumulative IMFs of 1-6to 1-12, the AF group exhibits a total lack of complexity in thecoarse-graining scales.

FIG. 14D presents the contrast between the healthy elder subject groupand the CHF group. The patterns are qualitatively similar to thecontrast between the healthy young subject group and the CHF group: anoverwhelmingly greater complexity for the healthy elder subject groupthan the CHF group, with a few exceptional scales. Some areas on fewexceptional scales in FIG. 14D has drastically transformed from lightergray to darker gray, this might represent drastic changes in the CHFgroup. FIG. 14E presents the contrast between the healthy elder subjectgroup and the AF group. Again, the patterns are the same as those inFIG. 14C, except that the respiration modulation is weaker in the AFgroup in FIG. 14E.

FIG. 14F presents the contrast between the CHF group and the AF group.The differences in FIG. 14F are in every scale. Even though the CHFgroup has suffered loss of complexity, they are still more complex thanthe AF group.

FIG. 13A-13D and FIG. 14A-14F illustrate the prowess and robustness ofiMSE. Thus, the iMSE provided by the present disclosure is a powerfultool for the visualization, comparison, or diagnosis of cardiovasculardisorders.

The embodiments shown and described above are only examples. Manydetails are often found in the art such as the other features of acircuit board assembly. Therefore, many such details are neither shownnor described. Even though numerous characteristics and advantages ofthe present technology have been set forth in the foregoing description,together with details of the structure and function of the presentdisclosure, the disclosure is illustrative only, and changes may be madein the detail, including in matters of shape, size and arrangement ofthe parts within the principles of the present disclosure up to, andincluding the full extent established by the broad general meaning ofthe terms used in the claims. It will therefore be appreciated that theembodiments described above may be modified within the scope of theclaims.

What is claimed is:
 1. A non-transitory computer program productembodied in a computer-readable medium and, when executed by one or moreanalysis modules, providing a visual output for presenting physiologicalsignals of a cardiovascular system, comprising: a first axisrepresenting subsets of intrinsic mode functions (IMFs); a second axisrepresenting a function of signal strength in a time interval; and aplurality of visual elements, each of the visual elements being definedby the first axis and the second axis, and each of the visual elementscomprising a plurality of analyzed data units collected over the timeinterval, wherein each of the analyzed data units comprises a firstcoordinate, a second coordinate, and a probability density valuegenerated from an intrinsic probability density function of one of thesubsets of IMFs, the first coordinate is one of the subsets of IMFs, andthe second coordinate is an argument of the function of signal strength.2. The non-transitory computer program product of claim 1, wherein thesecond axis is a standard deviation or a z-value of the signal strengthin the time interval.
 3. The non-transitory computer program product ofclaim 1, wherein the probability density value is generated from asubset of primary IMFs or secondary IMFs, each of the primary IMFs isgenerated from an empirical mode decomposition (EMD) of a plurality ofthe physiological signals, and each of the secondary IMFs is generatedfrom an EMD of the primary IMF.
 4. The non-transitory computer programproduct of claim 1, wherein the physiological signals areelectrocardiography (EKG) signals, electromyography (EMG) signals, orblood pressure signals.
 5. The non-transitory computer program productof claim 1, wherein the probability density value is indicated bydifferent colors, grayscales, dot densities, contour lines, orscreentones.
 6. A system for analyzing physiological signals of acardiovascular system, comprising: a detection module for detecting thephysiological signals of the cardiovascular system; a transmissionmodule for receiving the physiological signals from the detection moduleand transmitting the physiological signals to the analysis module; ananalysis module for generating a plurality of analyzed data sets fromthe physiological signals, each of the analyzed data sets comprising aplurality of analyzed data units; and a visual output module forrendering a visual output space according to the analyzed data setsgenerated by the analysis module, and displaying a visual output,wherein the visual output comprises a first axis representing subsets ofintrinsic mode functions (IMFs), a second axis representing a functionof signal strength in a time interval, and a plurality of visualelements defined by the first axis and the second axis, and each of thevisual elements comprises a plurality of analyzed data units collectedover the time interval, and each of the analyzed data units comprises afirst coordinate, a second coordinate, and a probability density valuegenerated by an intrinsic probability density function of one of thesubsets of IMFs, the first coordinate is one of the subsets of IMFs, andthe second coordinate is an argument of the function of signal strength.7. The system of claim 6, wherein the second axis is a standarddeviation or a z-value of the signal strength in the time interval. 8.The system of claim 6, wherein the probability density value isgenerated from a subset of primary IMFs or secondary IMFs, each of theprimary IMFs is generated from an empirical mode decomposition (EMD) ofa plurality of the physiological signals, and each of the secondary IMFsis generated from an EMD of the primary IMF.
 9. The system of claim 6,wherein the physiological signals are electrocardiography (EKG) signals,electromyography (EMG) signals, or blood pressure signals.
 10. Thesystem of claim 6, wherein the probability density value is indicated bydifferent colors, grayscales, dot densities, contour lines, orscreentones.
 11. A non-transitory computer program product embodied in acomputer-readable medium, and when executed by one or more analysismodules, providing a visual output for presenting physiological signalsof a cardiovascular system, comprising: a first axis representing ascale of intrinsic multiscale entropy (iMSE); a second axis representingcumulative intrinsic mode functions (IMFs); and a plurality of visualelements, each of the visual elements being defined by the first axisand the second axis, and each of the visual elements comprising ananalyzed data unit collected over a time interval, wherein each of theanalyzed data units comprises a first coordinate of the first axis, asecond coordinate of the second axis, and an iMSE value generated fromthe IMFs.
 12. The non-transitory computer program product of claim 11,wherein the IMFs are a set of primary IMFs or a set of secondary IMFs,each of the primary IMFs is generated from an empirical modedecomposition (EMD) of a plurality of the physiological signals, andeach of the secondary IMFs is generated from an EMD of the primary IMF.13. The non-transitory computer program product of claim 11, wherein thephysiological signals are electrocardiography (EKG) signals,electromyography (EMG) signals, or blood pressure signals.
 14. Thenon-transitory computer program product of claim 11, wherein the iMSEvalue is indicated by different colors, grayscales, dot densities,contour lines, or screentones.
 15. A system for analyzing physiologicalsignals of a cardiovascular system, comprising: a detection module fordetecting the physiological signals of the cardiovascular system; atransmission module for receiving the physiological signals from thedetection module and transmitting the physiological signals to theanalysis module; an analysis module for generating a plurality ofanalyzed data sets from the physiological signals, each of the analyzeddata sets comprising a plurality of analyzed data units; and a visualoutput module for rendering a visual output space according to theanalyzed data sets generated by the analysis module, and displaying avisual output, wherein the visual output comprises a first axisrepresenting a scale of intrinsic multiscale entropy (iMSE), a secondaxis representing cumulative intrinsic mode functions (IMFs), and aplurality of visual elements defined by the first axis and the secondaxis, and each of the visual elements comprising an analyzed data unitcollected over a time interval, and each of the analyzed data unitscomprises a first coordinate of the first axis, a second coordinate ofthe second axis, and an iMSE value generated from the IMFs.
 16. Thesystem of claim 15, wherein the IMFs are a set of primary IMFs or a setof secondary IMFs, each of the primary IMFs is generated from anempirical mode decomposition (EMD) of a plurality of electrical activitysignals, and each of the secondary IMFs is generated from an EMD of theprimary IMF.
 17. The system of claim 15, wherein the physiologicalsignals are electrocardiography (EKG) signals, electromyography (EMG)signals, or blood pressure signals.
 18. The system of claim 15, whereinthe iMSE value is indicated by different colors, grayscales, dotdensities, contour lines, or screentones.